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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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New upper bounds for kissing numbers from semidefinite programming
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by Christine Bachoc and Frank Vallentin PDF
J. Amer. Math. Soc. 21 (2008), 909-924 Request permission

Abstract:

Recently A. Schrijver derived new upper bounds for binary codes using semidefinite programming. In this paper we adapt this approach to codes on the unit sphere and we compute new upper bounds for the kissing number in several dimensions. In particular our computations give the (known) values for the cases $n = 3, 4, 8, 24$.
References
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Additional Information
  • Christine Bachoc
  • Affiliation: Laboratoire A2X, Université Bordeaux I, 351, cours de la Libération, 33405 Talence, France
  • Email: bachoc@math.u-bordeaux1.fr
  • Frank Vallentin
  • Affiliation: Centrum voor Wiskunde en Informatica (CWI), Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
  • Email: f.vallentin@cwi.nl
  • Received by editor(s): October 17, 2006
  • Published electronically: November 29, 2007
  • Additional Notes: The second author was supported by the Netherlands Organization for Scientific Research under grant NWO 639.032.203 and by the Deutsche Forschungsgemeinschaft (DFG) under grant SCHU 1503/4-1.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 21 (2008), 909-924
  • MSC (2000): Primary 52C17, 90C22
  • DOI: https://doi.org/10.1090/S0894-0347-07-00589-9
  • MathSciNet review: 2393433